Program Synthesis is the task of generating a program from a provided specification. Traditionally, this has been treated as a search problem by the programming languages (PL) community and more recently as a supervised learning problem by the machine learning community. Here, we propose a third approach, representing the task of synthesizing a given program as a Markov decision process solvable via reinforcement learning(RL). From observations about the states of partial programs, we attempt to find a program that is optimal over a provided reward metric on pairs of programs and states. We instantiate this approach on a subset of the RISC-V assembly language operating on floating point numbers, and as an optimization inspired by search-based techniques from the PL community, we combine RL with a priority search tree. We evaluate this instantiation and demonstrate the effectiveness of our combined method compared to a variety of baselines, including a pure RL ablation and a state of the art Markov chain Monte Carlo search method on this task.